Bayesian persuasion with optimal learning

Abstract

We study a model of Bayesian persuasion between a designer and a receiver with one substantial deviation from the standard setup—the designer offers once and for all a single statistical experiment from which the receiver can acquire costly i.i.d. signals over time. Taking a 2-state-2-action environment and employing a tractable continuous-time framework, we fully characterize the optimal persuasion policy. When the receiver features high skepticism, the optimal policy is to immediately reveal the truth, which is true for a large set of primitives. We construct the designer’s maximum payoff and find a discontinuous drop in it as compared with the standard model. Unlike in many standard persuasion models, the designer is not able to appropriate all the rents of information disclosure while the receiver often achieves the highest possible benefit from being able to repeatedly sample from the strategically offered information structure.